Emanuele Alesci

The Complete LQG propagator. II. Asymptotic behavior of the vertex

In a previous article we have shown that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit.

Quantum-Reduced Loop Gravity: Cosmology

We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.

A regularization of the hamiltonian constraint compatible with the spinfoam dynamics

We introduce a new regularization for Thiemanns Hamiltonian constraint. The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearance of the 15j Wigner symbol in these.

Asymptotics of loop quantum gravity fusion coefficients

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into

Quantum reduced loop gravity: Universe on a lattice

SU(2)_L\times SU(2)_R

Matrix elements of Lorentzian Hamiltonian constraint in loop quantum gravity

semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into

Intertwiner dynamics in the flipped vertex

SU(2)_L\times SU(2)_R

Quantum-Reduced Loop-Gravity: Relation with the Full Theory

semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.

Quantum reduced loop gravity and the foundation of loop quantum cosmology

We describe the quantum flat universe in QRLG in terms of states based at cuboidal graphs with six-valent nodes. We investigate the action of the scalar constraint operator at each node and we construct proper semiclassical states. This allows us to discuss the semiclassical effective dynamics of the quantum universe, which resembles that of LQC. In particular, the regulator is identified with the third root of the inverse number of nodes within each homogeneous patch, while inverse-volume corrections are enhanced.

Curvature operator for loop quantum gravity

The Hamiltonian constraint is the key element of the canonical formulation of LQG coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so called Euclidean and Lorentzian parts. However, due to the high complexity of this operator, only the matrix elements of the Euclidean part have been considered so far. Here we evaluate the action of the full constraint, including the Lorentzian part. The computation requires an heavy use of SU(2) recoupling theory and several tricky identities among n-j symbols are used to find the final result: these identities, together with the graphical calculus used to derive them, also simplify the Euclidean constraint and are of general interest in LQG computations.